Menu Close

Calculate-the-quadruple-integralas-follows-I-0-1-0-x-0-y-0-z-sin-x-2-y-2-z-2-w-2-1-w-2-z-2-dw-dz-dy-dx-




Question Number 211703 by MrGaster last updated on 17/Sep/24
   Calculate the quadruple   integralas follows:              I=∫_0 ^1 ∫_0 ^x ∫_0 ^y ∫_0 ^z ((sin(x^2 +y^2 +z^2 +w^2 ))/(1+w^2 +z^2 ))dw dz dy dx
$$ \\ $$$$\:\mathrm{Calculate}\:\mathrm{the}\:\mathrm{quadruple}\: \\ $$$$\mathrm{integralas}\:\mathrm{follows}: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\boldsymbol{{I}}=\int_{\mathrm{0}} ^{\mathrm{1}} \int_{\mathrm{0}} ^{\boldsymbol{{x}}} \int_{\mathrm{0}} ^{\boldsymbol{\mathrm{y}}} \int_{\mathrm{0}} ^{\boldsymbol{{z}}} \frac{\boldsymbol{\mathrm{sin}}\left(\boldsymbol{{x}}^{\mathrm{2}} +\boldsymbol{\mathrm{y}}^{\mathrm{2}} +\boldsymbol{{z}}^{\mathrm{2}} +\boldsymbol{{w}}^{\mathrm{2}} \right)}{\mathrm{1}+\boldsymbol{{w}}^{\mathrm{2}} +\boldsymbol{{z}}^{\mathrm{2}} }\boldsymbol{{dw}}\:\boldsymbol{{dz}}\:\boldsymbol{\mathrm{dy}}\:\boldsymbol{{dx}} \\ $$$$ \\ $$
Commented by MrGaster last updated on 17/Sep/24
Calculate the integrals in the areas 0≤w≤z, 0≤z≤y, 0≤y≤x, 0≤x≤1, where the function of the integral is sin (x 2+y 2+z 2+w 2) divided by (1+w^2+z^2).
Commented by BHOOPENDRA last updated on 18/Sep/24
I≈0.41176??
$${I}\approx\mathrm{0}.\mathrm{41176}?? \\ $$

Leave a Reply

Your email address will not be published. Required fields are marked *